A fast-food restaurant chain has 633 outlets in the United States. The following table categorizes them by city population and location and presents the number of outlets in each category. An outlet is chosen at random from the 633 to test market a new menu.
$\begin{array}{ccccc}
\hline &{\text { Region }} \
\hline \text { Population } & & & & \
\text { of city } & \text { NE } & \text { SE } & \text { SW } & \text { NW } \
\text { Under } 50,000 & 28 & 30 & 31 & 22 \
50,000-500,000 & 58 & 46 & 54 & 42 \
\text { Over 500,000 } & 79 & 125 & 74 & 44 \
\hline
\end{array}$
Given that the outlet is located in a city with a population under 50,000 , what is the probability that it is in the Southwest?
A) 0.27
B) 0.175
C) 0.279
D) 0.049

Question

Quizplus · Accepted Answer

To find the probability that the outlet is in the Southwest given it is located in a city with a population under 50,000, we use the formula for conditional probability. The number of outlets in cities with a population under 50,000 is 28 (NE) + 30 (SE) + 31 (SW) + 22 (NW) = 111. The number of outlets in the Southwest in cities under 50,000 is 31. Therefore, the probability is 31/111 = 0.279.

A Fast-Food Restaurant Chain Has 633 Outlets in the United